We find out that Oblonsky got his job through a family connection (his sister Anna's husband). Even if that job hadn't been available, someone else would have helped him out, because he's well-connected.
Apparently, Oblonsky knows half of Moscow and St. Petersburg. He's a great guy and everyone likes him. And besides, that's just how things work in 1870s Russian society: cronyism everywhere.
Everyone, everywhere, likes Prince Oblonsky, primarily for three reasons: 1) since he knows his own faults, he's extremely willing to forgive everyone else for theirs; 2) he behaves in an egalitarian fashion, meaning that he treats everyone the same, and 3) he never gets excited about his job and he never makes mistakes.
During his council meeting, there is activity at the door.
Oblonsky wants to know who's there.
The doorkeeper points out a big man with a curly beard and a sheepskin hat, whom Oblonsky greets with great affection.
The man turns out to be Constantine Levin (keep your eye on this character—he's one of the major protagonists).
Oblonsky and Levin are childhood friends who took different paths in life. Oblonsky is urbane and self-assured, while Levin lives in the country and is socially awkward and shy.
A characteristically awkward social encounter occurs when Levin is introduced to Oblonsky's colleagues, Philip Nikitin and Michael Grinevich.
Levin is described as a member of District Council, a cattle breeder, and a hunter. He is also introduced as Sergius Koznyshev's brother. (Sergius Koznyshev is a well-known writer.) Levin isn't too pleased about this last bit, because he hates being known as the "brother of Sergius Koznyshev."
Also, it turns out that he has quit the District Council.
Levin blushes furiously when Oblonsky notes that Levin is wearing a new French suit. Levin then insists that the two of them have a private chat.
After Oblonsky suggests dinner, Levin demurs, arguing that he doesn't have that much to say.
So Oblonsky tells Levin to say what he needs to say.
Levin becomes shy, and then finally asks what the Shcherbatskys (those are Oblonsky's in-laws) are up to.
Oblonsky knows that Levin is in love with Kitty, the youngest Shcherbatsky girl, (who also happens to be Dolly's younger sister.)
Oblonsky tells Levin that he can't give a short answer to the question.
They agree to talk later. Levin blushes a lot.
Oblonsky tells Levin to go to the zoo where Kitty skates. Oblonsky will pick Levin up for dinner there.
Levin dashes out, realizing later that he forgot to say good-bye to Oblonsky's colleagues.
We also find out that Levin owns six thousand acres of land in the Karazin District.